the radical rational…

in search of innovative ideas with a well-balanced approach for the math classroom

Triangles, Toothpicks and Patterns

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This was our visual pattern in Algebra 1 today. 
They were upset because there were so many triangles. And so many toothpicks.  Which then means…there were so many patterns.

But the way they saw it was much different than how I saw it.  So I listened.

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J: But where are you getting the triangles?  Here’s what I see…

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And there was a discussion of the center “upside down” triangles (yep, they said it)…do we count them? They’re like bonus triangles, you really don’t build those, they just happen.  Hmm? Really.

Someone would make a suggestion for finding toothpicks and we would try it…if not, let’s look again.

Z: It’s easier if we don’t count them to find the pattern for number of toothpicks.  You add the new step # to last triangle # then each one takes 3 toothpicks.

Okay…so what about step 27? And step 43?

And it was fun watching them struggle a little.

K:  If you add the step # to the steps before, you get triangles you build.

And I see using triangular numbers and arithmetic series discussion in our future? 

Why? Because it’s next in our curriculum? No. Because they are engaged in this question.

They kept seeing patterns and describing them.  They were playing with their math.  And it made me smile.

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Class Clipboards #made4math

Last Friday we had a teacher day…no students, but many things to get accomplished.  Contrary to what many think, it was a busy day.  No, we didn’t get “the day off.”

As I completed my self-reflection prior to writing my PGP, I realized 4B, maintaining accurate records was an area I wanted to improve. 

I have used a similar system for several years.  A spreadsheet to take attendance, record class notes/observations, quiz levels, etc.  But the downfall, it was on a weekly basis.  I kept a stapled copy of all of my classes on a clipboard.  If I needed to look back for a specific class to last Thursday, I had to rustle through all classes to find it.

I updated my form, landscape format.  There are 2 columns for each day.  One for attendance, one for behavior, etc.  I have more columns to the right to record target quiz results, notes for tutoring, etc.

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This looks very similar to a post I read earlier in the year…thanks for sharing, I am sorry I can’t remember who to tag.  I had just enough clipboards in a tote and tied on a ribbon for each class.  This way I will keep multiple weeks for a single class on the clipboard, when I have a specific question or student, I can flip through to find exactly what I need.

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Agree / Disagree Post-its

Students submitted an answer to an assigned question on a post-it note.

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Post-its were placed around the room. Each person visited each answer comparing to their own.  If they agreed, there was a tally mark added to A, if not, to D.  A quick self-assessment, without me reading off every answer.

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It eliminated having to discuss questions everyone got correct.  We could spend time on “issues” like #4.

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Personal Reflection 3-2-1 #MTBoSchallenge

Our school district will begin using a new Certified Evaluation Plan this year.  The CEP has 2 major components: Professional Practice and Student Growth.  As part of the Professional Practices, each teacher is asked to consider various pieces of evidence and complete a self reflection which eventually leads to their individual Professional Growth Plan.

I will be completing my self reflection this upcoming week, which has had me wondering this weekend, what are my goals for this school year? 

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3 things I want to learn, incorporate, practice:
I have read about Flipped Classrooms since before I began blogging.  Watched a couple webinars, read several blog posts, articles.  Its always been of interest, but I just didn’t have take the time.  I have recently begun my first Flipped Unit in my Algebra 2s.  It nothing major, I have linked to videos readily available on You Tube, but have quickly learned if students are accessing on their school accounts, YouTube is blocked.  So I am now looking for possible places to host my own videos (eventually, I want to use my own).   

My interpretation is either introduction or skills needed for problem solving which in turn allows students time in class for real application of math.  Following each video, I include 3-5 questions of the big ideas/takeaways for student self-assessment of the video.  When I begin creating my own, I intend to keep them around the 4 minute range, continue including self-assess questions.  For student who dont have access, they can come to my classroom prior to school/class and complete, but they are not allowed to participate in the days activities until they’ve completed the video or shown understanding to me.

Lesson Study – I have read some posts, been involved in a few informal twitter chats, even discussed the process with colleagues at TMC14.  I have located some resources through our PD360 I intend to utilize, but now, I have to find a friend and convince them its worthwhile to journey with me.

Talking Points -I want to ensure that every student feels like they can share their ideas and be heard.  Talking Points is the key for me developing this culture of learning.  I look forward to learning more, sharing with my students and implementing this as a classroom norm.  Here is a place to start.  Severval MtBoS have implemented them as the school year began.  I will share my experiences soon!

2 things I want to continue improving:
Literacy in Math Class- Whether reading, interpretting/deciphering informational text, writing, reflecting on their learning, verbally communicating or strategies to help studentsconnect vocabulary to prior knowledge…communication is a key skill they can use elsewhere.  Last spring, I participated in a webinar based on the book Vocabulary Their Way.  I sincerely feel providing students with similar tools will enhance their learning across all discilpines.  I plan to use some of the structures I’ve learned from Kagan resources and develop some of my own activities for student interaction with peers.

Standards Based Grading – about 5 years ago, I became very interested in aspects of Standards Based Grading.  It just made sense.  I had read, researched, even implemented some successful approaches.  I have heard through the grapevine, theres a possile push for our district to move this direction.  Even though it has not come from an official administrator, I’ve heard teacher conversations outside of vertical meetings that sounds like it may be on it’s way.  I am uber excited.  I have been looking for some good quality resources to share, should the time arise.  @mpershan shared a link this morning for a couple of good resources.  Scroll down to Garry Chu SBG.  Although, I think the Jeff Harding’s video following it gives a fun analogy to show how ridiculous some of our grading practices are-supporting Why we should consider SBG, then Mr. Chu shares some great ideas on How to implement.  I look forward to getting to move on this journey again (finally).

1 thing that’s Imperative in My Planning…
Standards of Mathematical Practices Yes, I am very familiar with them, yet I have not been so intentional in my planning and inclusion of them.  I had a major a-ha last year that I had missed the boat when first becoming familiar with CCSS.  The SMP should have been the anchoring foundation prior to transitioning to CCSS.  As I plan this year, I will be intentional and very explicit in providing students opportunities to use them.  But also in asking students to reflect on their uses of them.  I look forward to reading NCTM’s Principles to Actions, hoping it will guide me in this goal.  Another resource I plan to revisit is Making Thinking Visible.  I read it a couple of years ago, but feel it provides quality routines to enhance student learning that support the SMP.

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Ten Frames – a Tool for My Students

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Student Led Discussions, but wait a minute…

As I read this article, I wondered, how often do I engage in rich discussions with colleagues?

Yes, I feel comfortable with my online PLN, and I have a handful of colleagues who don’t gawk at me when I start talking about a book or article I read.  But for the most part, I avoid saying things when I am around certain people because the conversation doesn’t continue.  Uncomfortable silence. 

That’s why I find myself avoiding it altogether. 

I wonder if I followed an idea like #eduread and shared an article with colleagues, something doable that’s not an entire book…to read prior to our PLC. 

  It seems when I ask for suggestions, nothing.  I don’t know if this is because they don’t want to do it, or really aren’t sure where to start.  So I let it go. And that’s not effective leadership. I suppose I am paranoid, not wanting others to feel that I am judging their teaching when I suggest an article.  I honestly want to talk, discuss, share ideas…so I can have better learning opportunities for my students.

Anyway, how do you start rich conversations with colleagues? 

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VNPS First Attempt

Our first attempt at vertical, non permanent surfaces…

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This was actually the 3rd task in this formative assessment lesson from MARS.  It actually falls under middle school lessons, but based on student assessment data and some informal questioning in class, this is exactly what my students need in developing some foundational understanding.

Round 1 was in pairs, they worked with % statements.

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Before we began round 2, I wrote $100 and $200 on the board and asked…what can I multiply 100 by to get 200.  They all laughed, ah, that’s easy Mrs. Wilson! 

Okay.  What about changing the direction? What can we multiply 200 by to get 100?

Divide it by 2! 

No. That’s not what I asked.  What can I multiply it by?

Silence.

Punching buttons.

.5!

Okay.

What about 150 to 160?

Silence.
Silence.
Punching buttons.
Silence.
This one’s hard.
Punching. Punching.
I’m getting close.

Finally.  Someone showed me their answer and asked, will you accept this? It’s very close.

Ok.

Others kept working.
I passed out the decimal cards and they completed this task individually.

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Still a few mishaps that led to discussion along the way.

When they returned from lunch, I had the new set of purple cards, fractions (oh my) with white boards and one marker per pair.

It took them a few minutes to get settled in.  You’re letting us write on the big boards? Yes! Although a couple had smaller boards in the window sills. 

Doodle. Doodle. Doodle.

But once they got started, it was great listening to them.  They quickly began picking up on patterns.

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Yes, a couple of groups will be energetic whether standing or sitting but they were on task for the most part.  There is still some discussions to wrap up but I am pleased with questions they asked, realizations and patterns they noticed.

I look forward to referring back to this foundational understanding in the future.

Percents Lessons Link

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Why Does This Work? Qs about Determinants

We have an Intro to Matrix Operations at the beginning of Algebra 2. 

Here’s my unit organizer.  Targets are based on Quality Core Standards.

I remember being shown this trick to use “determinants” to find area of polygons in a plane.

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But why does it work?  Sure it’s a nice quick trick, but why?

Also, we evaluate determinants and use them to find inverses…but what is the value really?  What have I actually found when I do this process?

Maybe I once knew.  I don’t know now.  But I’d like to know why because my kids will ask.   And I want to do better than in the past.

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Reading…without a Library

With renovations in full swing, our school library is currently boxed up. 

Our ELA folks were squirming,  what would their student’s read during this time?

They contacted our Public Library, met with them, devised a plan…and voila!

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Our temporary library!  The folks set up accounts for our students, complete with scan card and key tags, shared with them how to check out ebooks on their devices and provided nearly 500 books considering student levels and interests.

It as begun for only a few classes this week but once all kinks are worked out, they will expand to all ELA classes.

What a great community connection out ELA folks have made – even introducing the public library to some students.

This is definitely a win-win for our school and community!

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The Wave

The class that challenged me the most yesterday is the one that made me smile the most today.

A snippet from their class…Yes I asked quest I ns, but so did they!

We collected data doing “The Wave.”  We talked about what we noticed.  Then I asked, who would want data like this and how would they use it?

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Student:  Maybe someone who wanted to know how long it would take all the people at a ballgame to do the wave.

So we guessed how long it would take 882 students.  And discussed different ways to make a prediction based on the data.

They decided to calculate each trial’s rate, then average them.  

Another student asked, how much space would it take for everyone to line up? 

I don’t know. How could we figure that out?

Student: Let’s see how much space we take up.

20 ft for 9 students. (Yes, that’s how small my class was today).

What made me smile…
Group 2:  K got an answer of 24 feet.  A: K, I disagree because if 20 feet is for 9 people, 24 isn’t much larger and that’s way too small for 882 people.  So they reworked.

Group 3: J: I got 1960 ft.  I asked the others, how’d J get this?  And they explained it to me.

Group 1: 16 miles.  (Huh?)

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And they shared their work. (20)(9)=180 (882)=79860 feet. 
S: I don’t understand where 180 came from?

C: can you explain why you multiplied 20 and 9?

A: what if you tried dividing those numbers and see if that works?

I loved how A suggested to his team that they split 882 students into groups of 9 and each group gets 20 feet.

This may be too elementary for some folks reading.  But the fact that a class of students who despise math, who “can’t do math” did their math just fine.

They not only explained their reasoning but respectfully asked questions to critque the thinking of others.

I want them to experience success.  I want them to know I value their thinking.  I want them to learn. I want to challenge them. I want them to smile when they enter my classroom. 

Yes, the class that challenged me most yesterday made me smile today.

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